交换环上的w-P-平坦模及其应用

w-P-Flat Modules over Commutative Rings and Their Applications

利用交换环上的w-模理论对P-平坦模进行w-模化研究.首先引入交换环上w-P-平坦模的概念,并讨论w-P-平坦模的一些刻画和性质;其次作为应用,给出von Neumann正则环和p.p环(即每个主理想是投射理想的环)的一些新刻画.

We studied the w-module theoretic analogue of P-flat modules by using w-module theory over commutative rings. Firstly, we introduced the concept of w-P-flat modules over commutative rings and discussed several characterizations and properties of w-P-flat modules. Secondly, as applications of w-P-flat modules, we give some new characterizations of von Neumann regular rings and p.p rings(i.e., rings in which every principle ideal is a projective ideal).